Lower functions for asymmetric Lévy processes

In Suk Wee

doi:10.1007/BF01203165

Lower functions for asymmetric Lévy processes

In Suk Wee

* Honorary professors

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Let {X_t} be a ℝ¹ process with stationary independent increments and its Lévy measure v be given by v{y:y>x}=x^-αL₁(x), v{y:y<-x}=x^-αL₂(x) where L₁, L₂ are slowly varying at 0 and ∞ and 0<α≦1. We construct two types of a nondecreasing function h(t) depending on 0<α<1 or α=1 such that lim inf {Mathematical expression} a.s. as t→ 0 and t→∞ for some positive finite constant C.

Original language	English
Pages (from-to)	469-488
Number of pages	20
Journal	Probability Theory and Related Fields
Volume	85
Issue number	4
DOIs	https://doi.org/10.1007/BF01203165
Publication status	Published - 1990 Dec

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/BF01203165

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title = "Lower functions for asymmetric L{\'e}vy processes",

abstract = "Let {Xt} be a ℝ1 process with stationary independent increments and its L{\'e}vy measure v be given by v{y:y>x}=x-αL1(x), v{y:y<-x}=x-αL2(x) where L1, L2 are slowly varying at 0 and ∞ and 0<α≦1. We construct two types of a nondecreasing function h(t) depending on 0<α<1 or α=1 such that lim inf {Mathematical expression} a.s. as t→ 0 and t→∞ for some positive finite constant C.",

author = "Wee, {In Suk}",

year = "1990",

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doi = "10.1007/BF01203165",

language = "English",

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pages = "469--488",

journal = "Probability Theory and Related Fields",

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T1 - Lower functions for asymmetric Lévy processes

AU - Wee, In Suk

PY - 1990/12

Y1 - 1990/12

N2 - Let {Xt} be a ℝ1 process with stationary independent increments and its Lévy measure v be given by v{y:y>x}=x-αL1(x), v{y:y<-x}=x-αL2(x) where L1, L2 are slowly varying at 0 and ∞ and 0<α≦1. We construct two types of a nondecreasing function h(t) depending on 0<α<1 or α=1 such that lim inf {Mathematical expression} a.s. as t→ 0 and t→∞ for some positive finite constant C.

AB - Let {Xt} be a ℝ1 process with stationary independent increments and its Lévy measure v be given by v{y:y>x}=x-αL1(x), v{y:y<-x}=x-αL2(x) where L1, L2 are slowly varying at 0 and ∞ and 0<α≦1. We construct two types of a nondecreasing function h(t) depending on 0<α<1 or α=1 such that lim inf {Mathematical expression} a.s. as t→ 0 and t→∞ for some positive finite constant C.

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JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 4

ER -

Lower functions for asymmetric Lévy processes

Abstract

ASJC Scopus subject areas

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